Molecular theory of Langevin dynamics for active self-diffusiophoretic colloids

Area of Science:

• Colloid Science
• Chemical Physics
• Statistical Mechanics

Background:

• Active colloidal particles use self-diffusiophoresis for motion.
• Langevin equations describe particle dynamics but fail for small particles.
• Existing models are often postulated or derived from fluctuating hydrodynamics.

Purpose of the Study:

• To provide a fully microscopic derivation of Langevin equations for self-diffusiophoretic particles.
• To establish microscopic expressions for friction tensors and reaction rate coefficients.
• To describe active motion at small scales where continuum models are inadequate.

Main Methods:

• Microscopic derivation of Langevin equations.
• Analysis of chemical reactions catalyzed asymmetrically by colloids.
• Use of generalized transport equations for fluid fields.

Main Results:

• Microscopic expressions for translational and rotational friction tensors.
• Microscopic expressions for reaction rate coefficients.
• Diffusiophoretic force and torque derived from nonequilibrium fluid field averages.

Conclusions:

• The derived Langevin equations accurately describe active motion of small colloids.
• This work extends the applicability of Langevin equations to nanoscale active matter.
• Provides a foundation for understanding microswimmer behavior at the molecular level.